Predicting the Tails of Breakthrough Curves in Regional-Scale Alluvial Systems by Yong Zhang 1 , David A. Benson 2 , and Boris Baeumer 3 Abstract The late tail of the breakthrough curve (BTC) of a conservative tracer in a regional-scale alluvial system is explored using Monte Carlo simulations. The ensemble numerical BTC, for an instantaneous point source injected into the mobile domain, has a heavy late tail transforming from power law to exponential due to a maximum thickness of clayey material. Haggerty et al.’s (2000) multiple-rate mass transfer (MRMT) method is used to pre- dict the numerical late-time BTCs for solutes in the mobile phase. We use a simple analysis of the thicknesses of fine-grained units noted in boring logs to construct the memory function that describes the slow decline of con- centrations at very late time. The good fit between the predictions and the numerical results indicates that the late-time BTC can be approximated by a summation of a small number of exponential functions, and its shape depends primarily on the thicknesses and the associated volume fractions of immobile water in ‘‘blocks’’ of fine- grained material. The prediction of the late-time BTC using the MRMT method relies on an estimate of the average advective residence time, t ad . The predictions are not sensitive to estimation errors in t ad , which can be approximated by L= v , where  v is the arithmetic mean ground water velocity and L is the transport distance. This is the first example of deriving an analytical MRMT model from measured hydrofacies properties to predict the late- time BTC. The parsimonious model directly and quantitatively relates the observable subsurface heterogeneity to nonlocal transport parameters. Introduction The dispersion of conservative solutes in natural porous media is often observed to be ‘‘anomalous,’’ which typically denotes non-Gaussian plume shapes and/or non- Fickian growth rates. Either phenomenon may lead to earlier and later arrival of solute at a control plane (i.e., the breakthrough curves [BTCs]) than those predicted for a homogeneous medium. Recent discussions of anom- alous laboratory scale and measured BTCs are given by Benson et al. (2001), Levy and Berkowitz (2003), Bromly and Hinz (2004), and Klise et al. (2004), among many others. Anomalous dispersion can be attributed to the long-range dependence (Dagan 1989) and high variance (Fogg 2004) of the permeability field. Because these two conditions are intrinsic characteristics of typical alluvial systems, a number of detailed studies of anomalous dis- persion have been conducted in alluvial aquifers. Gener- ally speaking, the networks of ancient stream channels can form preferential flow paths and cause early arrivals in BTCs, while the surrounding fine-grained aquitard materi- als sequester the solutes and result in late tails in BTCs (Fogg et al. 2000; LaBolle and Fogg 2001). Although transport coefficients have been shown numerically to be time-dependent in alluvial systems by LaBolle and Fogg (2001), the quantitative analyses of tailing behaviors of BTCs in regional-scale alluvial sys- tems are still needed, especially for practical problems involving a long timescale (decades to centuries) and a large space scale (hundreds to thousands of meters), such as ground water age dating (Weissmann et al. 2002), vulnerability assessment of regional aquifers (Fogg et al. 1998a), and evaluation of aquifer remediation by pump- and-treat techniques (LaBolle and Fogg 2001). Two methods 1 Department of Geology and Geological Engineering, Colo- rado School of Mines, Golden, CO 80401. 2 Corresponding author: Department of Geology and Geo- logical Engineering, Colorado School of Mines, Golden, CO 80401; (303) 273-3806; fax (303) 273-3859; dbenson@mines.edu 3 Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand. Received July 2006, accepted February 2007. Copyright ª 2007 The Author(s) Journal compilation ª 2007 National Ground Water Association. doi: 10.1111/j.1745-6584.2007.00320.x Vol. 45, No. 4—GROUND WATER—July–August 2007 (pages 473–484) 473